GAP implementation

Group ID

This finite group has order 24 and has ID 1 among the groups of order 24 in GAP's SmallGroup library. For context, there are 15 groups of order 24. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(24,1)

For instance, we can use the following assignment in GAP to create the group and name it :

gap> G := SmallGroup(24,1);

Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [24,1]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.